Problem: Simplify the following expression: $ z = \dfrac{-7x + 2}{10x + 10} - \dfrac{-6}{5} $
Explanation: In order to subtract expressions, they must have a common denominator. Multiply the first expression by $\dfrac{5}{5}$ $ \dfrac{-7x + 2}{10x + 10} \times \dfrac{5}{5} = \dfrac{-35x + 10}{50x + 50} $ Multiply the second expression by $\dfrac{10x + 10}{10x + 10}$ $ \dfrac{-6}{5} \times \dfrac{10x + 10}{10x + 10} = \dfrac{-60x - 60}{50x + 50} $ Therefore $ z = \dfrac{-35x + 10}{50x + 50} - \dfrac{-60x - 60}{50x + 50} $ Now the expressions have the same denominator we can simply subtract the numerators: $z = \dfrac{-35x + 10 - (-60x - 60) }{50x + 50} $ Distribute the negative sign: $z = \dfrac{-35x + 10 + 60x + 60}{50x + 50}$ $z = \dfrac{25x + 70}{50x + 50}$ Simplify the expression by dividing the numerator and denominator by 5: $z = \dfrac{5x + 14}{10x + 10}$